A strain of bacteria reproduces at the rate of 25% every 12 min.

Question

A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?

(A) 96 min
(B) 72 min
(C) 60 min
(D) 48 min 
(E) 40 min

Bunuel · Answer

A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?

(A) 96 min
(B) 72 min
(C) 60 min
(D) 48 min 
(E) 40 min

The original question is:
 A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?

1.25^x = 3 --> x = ~5 --> five 12 minute periods = 60 minutes.

Answer: C.

pretzel · Answer

Hi Bunnel,

I used rounding off method. Is that right?
1.25 approx 1.3
 1.3^2  = 1.69
 1.7^2  = 2.89 or approx 3

Since we squared twice and 1.3>1.25, we need more than 4, or at least 5.

KarishmaB · Answer

Responding to a pm:

If initial amount of bacteria is X, we need it to become 3X. How many 12 min time intervals does it need? Let's assume we need n time intervals.

X*(5/4)^n = 3X
(5/4)^n = 3

Now note that the options are 12*4, 12*5, 12*6 etc. So this gives us some ideas.

(5/4)^4 = 625/256 -> this is much less than 3 since 256*3 is more than 750.
(5/4)^5 = 3125/1024 -> this is a tiny bit more than 3 and hence is out answer since 1024*3 is a bit more than 3000.

Hence n is 5 and time required = 12*5 = 60 mins

arshu27 · Answer

Responding to a pm:

If initial amount of bacteria is X, we need it to become 3X. How many 12 min time intervals does it need? Let's assume we need n time intervals.

X*(5/4)^n = 3X
(5/4)^n = 3

Now note that the options are 12*4, 12*5, 12*6 etc. So this gives us some ideas.

(5/4)^4 = 625/256 -> this is much less than 3 since 256*3 is more than 750.
(5/4)^5 = 3125/1024 -> this is a tiny bit more than 3 and hence is out answer since 1024*3 is a bit more than 3000.

Hence n is 5 and time required = 12*5 = 60 mins

--------------
 i could not understand the solution at all. could you please explain as to how did you get the fraction 5/4?

KarishmaB · Answer

If a number has to be increased by 25%, you effectively multiply it by 5/4.

n + n*25/100 = n + n/4 = n(1 + 1/4) = n*5/4

Similarly, if you want to increase a number by 20%, you multiply it by 6/5 and so on...

Since the colony increases by 25% every 12 mins, you keep multiplying it by 5/4 till it becomes 3 times.

GMAT2645 · Answer

How are you able to see that (1.25)^x = 3 yields x = 5? Are you completing this calculation in your head? Thank you.

KarishmaB · Answer

Approximate.

(1.25)^2 = 1.5625 (square of a number ending in 5 is easy to find.

75^2 = _(7*8)_ 25 = 5625
35^2 = _(3*4)_25 = 1225
105^2 = _(10*11)_25 = 11025

Now round up 1.5625 to 1.6
1.6^2 = 2.56 (so this is about 1.25^4)

So we are close to 3 but not quite there yet.
Round down 2.56 to 2.5 and 1.25 to 1.2

2.5*1.2 = 3.00 = about 1.25^5

rahul16singh28 · Answer

Hi  VeritasPrepKarishma ,

Why cant we use GP Series here?? Can you please clarify.

Let x be initial bacteria. Now, we have

x + 5x/4 + 25x/16 + ... = 3x
(5/4)^n = 7/4..

However, I am not able to get value of n here.

KarishmaB · Answer

This is a compounding situation.

x becomes (5/4)x which becomes (5/4)^2x which then becomes (5/4)^3x and so on...

We cannot add these terms since once x becomes (5/4)x, we don't have x anymore.

raghavdev · Answer

Let's assume x (initial bacteria strain) = 100
x (final bacteria strain) = 300  
Time interval, T=12. 
At T=12, X (final) = 25%(100) = 125.
At T=24, X (final) = 25%(125) = ~156. 
At T=36, X (final) = 25%(156) = ~195.  
At T=48, X (final) = 25%(195) = ~244.
At T=60, X (final) = 25%(244) = ~305, which is closest to 300. Therefore at T=60 mins, X(final) = 300 = 3X.

vatsal323 · Answer

This is a compounding situation.

x becomes (5/4)x which becomes (5/4)^2x which then becomes (5/4)^3x and so on...

We cannot add these terms since once x becomes (5/4)x, we don't have x anymore.

Hey Karishma, I didn't understand this explanation. Why is there no x anymore?

I have the same doubt as Rahul. The question stem is not clear and the 25% increase could be from the newly acquired value after every new 12 min iteration, making it a GP/Compound Interest sorta problem. Why can't it be interpreted in that way?

bumpbot · Answer

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A strain of bacteria reproduces at the rate of 25% every 12 min.

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